Rewrite as a simplified fraction. ${1.1\overline{6} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 116.6666...\\ 10x &= 11.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 105}$ ${x = \dfrac{105}{90}} $ ${x = \dfrac{7}{6}} \text{or} {1 \dfrac{1}{6}}$